4. To determine if a triangle is a right triangle, given that you know the length of its sides, you have to check if its lengths follow the Pythagorean theorem.
This theorem states that the square of the hypothenuse (c) is equal to the sum of the squares of the legs of the triangle (a and b), following the expression:
The triangle is:
We have to check that a²+ b² is equal to c².
The square of the hypothenuse is:
The sum of the squares of the legs of the triangle is:
As you can see, the sum of the squares of the legs of the triangle is 100, which is the same as the square of the hypothenuse. The triangle follows the Pythagorean theorem and can be considered a right triangle.
Step-by-step explanation:
Answer:
Step-by-step explanation:
Simplifying
4x + 5 = 33
Reorder the terms:
5 + 4x = 33
Solving
5 + 4x = 33
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-5' to each side of the equation.
5 + -5 + 4x = 33 + -5
Combine like terms: 5 + -5 = 0
0 + 4x = 33 + -5
4x = 33 + -5
Combine like terms: 33 + -5 = 28
4x = 28
Divide each side by '4'.
x = 7
Simplifying
x = 7
<span>for the first part, realize that the hour and minute hands are moving at different rates; in one hour, the minute hands moves all the way around the face of the clock, and thus moves a total of 360 degrees or 2 pi radians; the hour hand moves only 1/12 away around the clock, so covers only 30 degrees or Pi/6 radians.
Now, the LINEAR distance traveled by the tip of each hand is also determined by the length of the hand. In the case of the minute hand, it sweeps out a circle of radius 10 cm, so traces out a circle of radius 10 cm. Since the circumference of a circle is 2*pi*r, the minute hand (remember it made one complete cycle) covers a distance of 2*pi*10cm=20 Pi cm
The hour hand covers only 1/12 a circle, but that circle is only 6 cm in radius, so the distance traveled by the tip of the minute hand is:
1/12 *[2 *pi*r]=1/12*[12*pi]=pi
so the difference is 19pi
for the last part, you should draw a diagram of the two hands, the minute hand is 10 cm in length, the hour hand is 6 cm in length, and they are 30 degrees apart...from that drawing, see if you can figure out the remaining leg of the triangle you can form from them
good luck</span><span>
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